Bulletin des Sciences Mathematiques最新文献

{"title":"The number of zeros of the sum of Abelian integrals satisfying two-dimensional Picard-Fuchs equations","authors":"Changjian Liu ,&nbsp;Shaoqing Wang","doi":"10.1016/j.bulsci.2025.103643","DOIUrl":"10.1016/j.bulsci.2025.103643","url":null,"abstract":"<div><div>This paper is primarily devoted to developing a new criterion to show the upper bound for the number of zeros of the sum of Abelian integrals satisfying two-dimensional Picard-Fuchs equations, which is a generalization of the method by Gavrilov and Iliev (2003) <span><span>[13]</span></span>. The second goal of this paper is to investigate, using our new criterion, the hyperelliptic Abelian integrals related to the period annuli of a Hamiltonian system <span><math><mover><mrow><mi>x</mi></mrow><mrow><mo>˙</mo></mrow></mover><mo>=</mo><mo>−</mo><mi>y</mi><mo>,</mo><mover><mrow><mi>y</mi></mrow><mrow><mo>˙</mo></mrow></mover><mo>=</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>(</mo><mi>x</mi><mo>)</mo></math></span> under the polynomial deformation of degree <em>n</em>, where <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>cos</mi><mo>⁡</mo><mo>(</mo><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mi>arccos</mi><mo>⁡</mo><mi>x</mi><mo>)</mo></math></span> is the Chebyshev polynomial of the first kind, and to show that for every period annulus of such system, the number of zeros of the hyperelliptic Abelian integral is no more than <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>, which is novel up to now.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"203 ","pages":"Article 103643"},"PeriodicalIF":1.3,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143903413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Compactness and related properties of weighted composition operators on weighted BMOA spaces","authors":"David Norrbo","doi":"10.1016/j.bulsci.2025.103642","DOIUrl":"10.1016/j.bulsci.2025.103642","url":null,"abstract":"<div><div>It is shown that a large class of properties coincide for weighted composition operators on a large class of weighted VMOA spaces, including the ones with logarithmic weights and the ones with standard weights <span><math><msup><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mrow><mo>|</mo><mi>z</mi><mo>|</mo></mrow><mo>)</mo></mrow><mrow><mo>−</mo><mi>c</mi></mrow></msup><mo>,</mo><mspace></mspace><mn>0</mn><mo>≤</mo><mi>c</mi><mo>&lt;</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>. Some of these properties are compactness, weak compactness, complete continuity and strict singularity. A function-theoretic characterization for these properties is also given. Similar results are also proved for many weighted composition operators on similarly weighted BMOA spaces. The main results extend the theorems given in Laitila et al. (2023) <span><span>[16]</span></span>, and new test functions that are suitable for the weighted setting are developed.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"203 ","pages":"Article 103642"},"PeriodicalIF":1.3,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143879063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Étude statistique du facteur premier médian, 3 : lois de répartition","authors":"Jonathan Rotgé","doi":"10.1016/j.bulsci.2025.103641","DOIUrl":"10.1016/j.bulsci.2025.103641","url":null,"abstract":"<div><div>We consider the Gaussian limit law for the distribution of the middle prime factor of an integer, defined according to multiplicity or not. We obtain an optimal bound for the speed of convergence, thereby improving on previous estimates available in the literature.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"203 ","pages":"Article 103641"},"PeriodicalIF":1.3,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143886313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Limit cycle bifurcations near double homoclinic and heteroclinic loops of a class of cubic Hamiltonian systems","authors":"Yanqin Xiong ,&nbsp;Xiang Zhang","doi":"10.1016/j.bulsci.2025.103640","DOIUrl":"10.1016/j.bulsci.2025.103640","url":null,"abstract":"<div><div>This paper studies the double homoclinic and heteroclinic bifurcations by perturbing a cubic Hamiltonian system with polynomial perturbations of degree <em>n</em>. It is proved that <span><math><mn>5</mn><mo>[</mo><mfrac><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>]</mo><mo>,</mo><mspace></mspace><mi>n</mi><mo>≥</mo><mn>3</mn></math></span> and <span><math><mn>2</mn><mo>[</mo><mfrac><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>]</mo></math></span> limit cycles can be bifurcated from the period annuli near the double homoclicic loop and the heteroclinic loop, respectively. This result improves the lower bound on the number of the bifurcated limit cycles comparing with the known results for the related problems. To achieve our results we develop the techniques on calculating the base and the relative relations of the elements in the base, formed partly by curve integral functions along ovals of level sets of the Hamiltonian function, which appear in the expansions of the first order Melnikov functions.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"201 ","pages":"Article 103640"},"PeriodicalIF":1.3,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143863705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Local second order horizontal Sobolev regularity for p-harmonic functions with Hörmander vector fields of step two","authors":"Chengwei Yu ,&nbsp;Yu Liu","doi":"10.1016/j.bulsci.2025.103636","DOIUrl":"10.1016/j.bulsci.2025.103636","url":null,"abstract":"<div><div>In this paper, we establish a trace inequality for any real symmetric square matrix and apply it to Hörmander vector fields of step two, which are denoted by <span><math><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span>. Let <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>≤</mo><mn>4</mn></math></span> when <span><math><mi>m</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn></math></span> and <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mn>3</mn><mo>+</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mi>m</mi><mo>−</mo><mn>2</mn></mrow></mfrac></math></span> when <span><math><mi>m</mi><mo>≥</mo><mn>4</mn></math></span>. Then we utilize the trace inequality to prove the horizontal Sobolev <span><math><msubsup><mrow><mi>W</mi></mrow><mrow><mi>X</mi><mo>,</mo><mrow><mspace></mspace><mi>loc</mi><mspace></mspace></mrow></mrow><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msubsup></math></span>-regularity of the weak solution <em>u</em> to the degenerate subelliptic <em>p</em>-harmonic equation <span><math><msub><mrow><mo>△</mo></mrow><mrow><mi>X</mi><mo>,</mo><mi>p</mi></mrow></msub><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>m</mi></mrow></munderover><msubsup><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mo>|</mo><mi>X</mi><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow></msub><mi>u</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></span>, namely, <span><math><mi>X</mi><mi>X</mi><mi>u</mi><mo>∈</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mrow><mspace></mspace><mi>loc</mi><mspace></mspace></mrow></mrow><mrow><mn>2</mn></mrow></msubsup></math></span>. Compared to the case of Euclidean spaces <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span> (<span><math><mi>m</mi><mo>≥</mo><mn>4</mn></math></span>), the range of this determined <em>p</em> is already optimal.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103636"},"PeriodicalIF":1.3,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143827751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Investigations of a class of Liouville-Caputo fractional order Pennes bioheat flow partial differential equations through orthogonal polynomials on collocation points","authors":"Vijay Saw ,&nbsp;Pratibhamoy Das ,&nbsp;Hari M. Srivastava","doi":"10.1016/j.bulsci.2025.103637","DOIUrl":"10.1016/j.bulsci.2025.103637","url":null,"abstract":"<div><div>In this study, we give a systematic discussion on convergent approximations of generalized nonlocal form of Pennes bioheat flow type parabolic partial differential equations. These flow problems frequently appear during the examination of the temperature variations in hyperthermia. Here, the nonlocal form involves Caputo-type fractional derivatives. The finite difference approximation in time is used on uniform steps to reduce the nondimensionalized form of the Pennes bioheat flow model into a semi-discrete continuous form in space. Thereafter, this semi-discrete problem is approximated by the third-kind shifted Chebyshev polynomials (TKSCP) on Chebyshev collocation points, at all time levels. This procedure converts the steady-state problem into a system of algebraic equations whose solution is the temperature distribution of the proposed model. In addition to the expected theoretical errors, a uniform convergence of the approximated solution to the exact solution is produced. We also investigated the effect of the order of fractional derivatives on the temperature distribution of living tissues computationally. Graphical results demonstrate that this generalized flow problem maintains a behavior similar to that of classical parabolic problems having integer-order partial derivatives when the fractional parameters tend to a positive integer.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"201 ","pages":"Article 103637"},"PeriodicalIF":1.3,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143830047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The existence of positive periodic solutions about generalized hematopoiesis model","authors":"Jia Yuan ,&nbsp;Lishan Liu ,&nbsp;Haibo Gu ,&nbsp;Yonghong Wu","doi":"10.1016/j.bulsci.2025.103638","DOIUrl":"10.1016/j.bulsci.2025.103638","url":null,"abstract":"<div><div>This paper focuses on the generalized hematopoietic model with multiple variable delays and multiple exponents. Using the fixed point theorem of cone expansion and compression, it is proved that the hematopoiesis model in the sup-linear or sub-linear case must have a positive periodic solution. And it is deduced that there are two positive periodic solutions for the hematopoietic model when it has both sup-linear and sub-linear terms. In addition, several examples of the numerical simulations are given in this paper for illustration.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103638"},"PeriodicalIF":1.3,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143859826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Seshadri constants of M‾0,n","authors":"Shripad M. Garge ,&nbsp;Arghya Pramanik ,&nbsp;Aditya Subramaniam","doi":"10.1016/j.bulsci.2025.103639","DOIUrl":"10.1016/j.bulsci.2025.103639","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mover><mrow><mi>M</mi></mrow><mo>‾</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>n</mi></mrow></msub></math></span> be the moduli space of stable rational <em>n</em>-pointed curves for <span><math><mi>n</mi><mo>≥</mo><mn>5</mn></math></span>. We estimate lower bounds for Seshadri constants of nef <span><math><mi>Q</mi></math></span>-line bundles at arbitrary points on <span><math><msub><mrow><mover><mrow><mi>M</mi></mrow><mo>‾</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>n</mi></mrow></msub></math></span> for <span><math><mn>5</mn><mo>≤</mo><mi>n</mi><mo>≤</mo><mn>7</mn></math></span>. Our results for <span><math><mi>n</mi><mo>=</mo><mn>5</mn></math></span> generalise some results of Taro Sano (2014). We also estimate lower bounds for Seshadri constants of nef Keel divisors at arbitrary points on <span><math><msub><mrow><mover><mrow><mi>M</mi></mrow><mo>‾</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>n</mi></mrow></msub></math></span> for <span><math><mi>n</mi><mo>≥</mo><mn>8</mn></math></span>, assuming a conjecture describing the Mori cone of <span><math><msub><mrow><mover><mrow><mi>M</mi></mrow><mo>‾</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>n</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103639"},"PeriodicalIF":1.3,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143859827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Infinitesimal and tangential 16-th Hilbert problem on zero-cycles","authors":"J.L. Bravo ,&nbsp;P. Mardešić ,&nbsp;D. Novikov ,&nbsp;J. Pontigo-Herrera","doi":"10.1016/j.bulsci.2025.103634","DOIUrl":"10.1016/j.bulsci.2025.103634","url":null,"abstract":"<div><div>In this paper, given two polynomials <em>f</em> and <em>g</em> of one variable and a 0-cycle <em>C</em> of <em>f</em>, we consider the deformation <span><math><mi>f</mi><mo>+</mo><mi>ϵ</mi><mi>g</mi></math></span>. We define two functions: the <em>displacement function</em> <span><math><mi>Δ</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>ϵ</mi><mo>)</mo></math></span> and its first order approximation: the <em>abelian integral</em> <span><math><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math></span>.</div><div>The <em>infinitesimal</em> and <em>tangential 16-th Hilbert problem</em> for zero-cycles are problems of counting isolated regular zeros of <span><math><mi>Δ</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>ϵ</mi><mo>)</mo></math></span>, for <em>ϵ</em> small, or of <span><math><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math></span>, respectively.</div><div>We show that the two problems are not equivalent and find optimal bounds, in function of the degrees of <em>f</em> and <em>g</em>, for the infinitesimal and tangential 16-th Hilbert problem on zero-cycles. These two problems are the zero-dimensional analog of the classical infinitesimal and tangential 16-th Hilbert problems for vector fields in the plane.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103634"},"PeriodicalIF":1.3,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143823856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Corrigendum to: Half-integrality of line bundles on partial flag schemes of classical Lie groups","authors":"Takuma Hayashi","doi":"10.1016/j.bulsci.2025.103626","DOIUrl":"10.1016/j.bulsci.2025.103626","url":null,"abstract":"<div><div>In this note, I fix mistakes on the continuity arguments concerning the profinite topology of the Galois group of an infinite Galois extension of fields in my previous paper <span><span>[6]</span></span>.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103626"},"PeriodicalIF":1.3,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143806592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}